More egg probabilities

Zethor · 9 Apr 2015 at 12:29

Inspired by this thread:

http://forums.overclockers.co.uk/showthread.php?t=18665294

A similar game, 1 normal egg, 5 boiled ones but only 1 player: Holly!

Each egg is has a number from 1 to 6.
Holly is asked to pick a number and let's say she chooses egg no. 1.
Before she tests it, it is revealed to her that egg no.6 is in fact boiled.
She is now given the chance to change her initial pick (pick an egg from 2 to 5) or continue with her initial choice - egg no. 1.

Should Holly change her egg or not?
Does her choice matter?

Zethor · 9 Apr 2015 at 12:50

Impy77 said:
Monty Hall.
Yes she should switch.

Are you sure about that?

Zethor · 9 Apr 2015 at 13:51

It looks a bit complicated at first glance but it's quite simple.

Her initial pick has 1/6 (~0.16) chance to be a normal egg. This means the rest of the eggs have 5/6 chances to be normal. When it is revelead that one of the 5 eggs is boiled, it's chance to be normal becomes zero. Thus, the 5/6 chance to be normal is now for the group of eggs 2,3,4 and 5. By changing her choice, she now has 1/4*5/6 (~0.2) chance to get the normal egg - higher than the initial 0.16 .

She doesn't want that so she should carry on with her initial choice.

Zethor · 11 Apr 2015 at 19:07

Cyberangel11 said:
If 6 is gone, egg 2 doesn't become less likely to win.

True but the rest of the eggs will be more likely to win.